At $10^{\circ} \mathrm{C}$ the value of the density of a fixed mass of an ideal gas divided by its pressure…

At $10^{\circ} \mathrm{C}$ the value of the density of a fixed mass of an ideal gas divided by its pressure is $\mathrm{x}$. At $110^{\circ} \mathrm{C}$ this ratio is
  1. $\frac{283}{383} x$
  2. $\mathrm{x}$
  3. $\frac{383}{283} x$
  4. $\frac{10}{110} x$

Solution

$\begin{aligned} P V & =n R T \\ & \Rightarrow P \cdot \frac{m}{\rho}=\frac{m}{M} R T \\ & \Rightarrow \frac{\left(\frac{\rho}{P}\right)_f}{\left(\frac{\rho}{P}\right)_i}=\frac{T_i}{T_f}=\frac{10+273}{110+273}=\frac{283}{383} \\ & \Rightarrow \frac{\left(\frac{\rho}{P}\right)_f}{x}=\frac{283}{383} \\ & \therefore\left(\frac{\rho}{P}\right)_f=\frac{283}{383} x \end{aligned}$ ^

Asked in: NEET 2008 (Mains)

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